We describe a research plan to develop an extended image formation model for single particle analysis and accompanying computational methods with the goal of achieving near atomic resolution in the electron microscopy structural studies of biological macromolecules. Although it has been possible to attain resolution finer than 10 A in a number of pilot studies, there are still no computational tools for routine high-resolution electron microscopy structure determination. Our goal is to advance the existing capabilities in order to extract 4-7 A resolution 3-D structures from the inherently noisy images of single particles by developing algorithms for robust and accurate image processing and error analysis. We demonstrate first that the current image formation model in electron microscopy is contradicted by the experimental evidence, and secondly that the massive data processing required for the high-resolution structure determination will be difficult to achieve using existing image processing tools. Within the framework of this proposal, we will detail and experimentally test an image formation model of electron microscopy that accounts for some non-linear effects. Specifically, we suggest that there should be a signal dependent noise, which therefore will depend on the relative amount of protein present on the grid. The new model will provide a basis for the signal-to-noise estimation for EM data and for improvements of alignment methods. In order to reduce the volume of the data we will develop a library of highly accurate algorithms for 3-D reconstruction from projections and for 2-D image manipulation using novel interpolation techniques. We will also develop algorithms for the calculation of the real space variance/covariance in structures reconstructed from sets of their projections. These methods are aimed at the localization of conformational variability using cryo-EM and at improving the accuracy of the docking of X-ray crystallographic domains into 3-D EM maps. The software will be developed in ways that assure full portability and will be disseminated throughout the EM community within the leading software packages SPARX and SPIDER.